四元数体上Cramer法则的两种证明

Identification of Cramer Ruler over Quaternion Field by Using Two Different Methods

将四元数体上n元线性方程组的求解问题转化为复数域上2n元线性方程组的求解问题。进而给出了四元数体上Cramer法则的两种较简单的证明。通过引入了一类特殊行列式的记号,由Cramer法则的两种证明过程得到了这类行列式的性质。

It is discussed that the solution of linear equations in n variables over quaternion field can be simplified into the solution of linear equations in 2n variables over complex field. Therefore, Cramer ruler is to be proven re- spectively by two different methods. Thus the property of some determinants over complex field is obtained by intro- ducing a sign from a class of determinants.